Noise-blocking banded earmuff devices include earmuffs with apertures that each receives the upper and middle part of the outer ear of a person, with the earlobe being pressed inwardly by the cushion that surrounds the aperture. Most cushion apertures are in the form of elongated ovals that efficiently receive the middle and upper parts of the outer ear. Usually, the band extends around the top of the person's head, or is angled backward by several degrees from an upward direction. Sometimes a person wishes to wear the band under his chin, which the elongated oval aperture allows. However, sometimes a person wishes to wear the band so it extends behind his head. If the earmuff cannot rotate on the band, then wearing the band behind a person's head results in the top of the outer ear being pressed inwardly by the cushion, which is generally uncomfortable and which reduces sound blocking. While the earmuffs can be mounted so they can rotate on the band ends, this adds to cost and size, especially if rugged mounting is to be achieved. A banded earmuff device that allows the band to extend behind a person's head as well as above the head and below the chin, without the earmuffs being rotatably mounted on the band ends, and using earmuffs of moderate size, would be of value.